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We experimentally analyzed the statistical errors in quantum-state estimation and examined whether their lower bound, which is derived from the Cramer-Rao inequality, can be truly attained or not. In the experiments, polarization states of…

Quantum Physics · Physics 2013-05-29 Koji Usami , Yoshihiro Nambu , Yoshiyuki Tsuda , Keiji Matsumoto , Kazuo Nakamura

This review aims at gathering the most relevant quantum multi-parameter estimation methods that go beyond the direct use of the Quantum Fisher Information concept. We discuss in detail the Holevo Cram\'er-Rao bound, the Quantum Local…

Quantum Physics · Physics 2020-09-02 Rafal Demkowicz-Dobrzanski , Wojciech Gorecki , Madalin Guta

Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyse bounds for the best position estimation of a stellar-like…

Instrumentation and Methods for Astrophysics · Physics 2016-10-26 Alex Echeverria , Jorge F. Silva , Rene A. Mendez , Marcos Orchard

It is shown that the condition for achieving the quantum Cramer-Rao bound of phase estimation in conventional two-path interferometers is that the state is symmetric with regard to an (unphysical) exchange of the two paths. Since path…

Quantum Physics · Physics 2009-03-17 Holger F. Hofmann

We derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic…

Quantum Physics · Physics 2019-05-09 Yuxiang Yang , Giulio Chiribella , Masahito Hayashi

We derive lower bounds on the variance of estimators in quantum metrology by choosing test observables that define constraints on the unbiasedness of the estimator. The quantum bounds are obtained by analytical optimization over all…

Quantum Physics · Physics 2023-07-27 M. Gessner , A. Smerzi

We find a large class of pure and mixed input states with which the phase estimation precision saturates the Cramer-Rao bound under the compound measurements of parity and particle number. We further propose a quantum-phase-estimation…

Quantum Physics · Physics 2019-04-23 Haijun Xing , Libin Fu , Su Yi

Minimum-variance estimators for the parameter fnl that quantifies local-model non-Gaussianity can be constructed from the cosmic microwave background (CMB) bispectrum (three-point function) and also from the trispectrum (four-point…

Cosmology and Nongalactic Astrophysics · Physics 2011-02-03 Marc Kamionkowski , Tristan L. Smith , Alan Heavens

The quantum Fisher information (QFI), as a function of quantum states, measures the amount of information that a quantum state carries about an unknown parameter. The (entanglement-assisted) QFI of a quantum channel is defined to be the…

Quantum Physics · Physics 2021-04-06 Sisi Zhou , Liang Jiang

Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of the phase shift. We compare the two frameworks and their sensitivity bounds to the estimation of…

Quantum Physics · Physics 2018-11-27 Yan Li , Luca Pezzè , Manuel Gessner , Weidong Li , Augusto Smerzi

We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…

Optics · Physics 2013-10-31 Shan Zheng Ang , Glen I. Harris , Warwick P. Bowen , Mankei Tsang

We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…

Instrumentation and Methods for Astrophysics · Physics 2015-11-18 Rodrigo A. Lobos , Jorge F. Silva , Rene A. Mendez , Marcos Orchard

-In this paper, we study Bayesian and hybrid Cramer-Rao bounds for the dynamical phase estimation of QAM modulated signals. We present the analytical expressions for the various CRBs. This avoids the calculation of any matrix inversion and…

Information Theory · Computer Science 2015-12-01 Jianxiao Yang , Benoit Geller , A Wei

Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies…

Statistics Theory · Mathematics 2025-08-26 Hayato Nishimori , Takeru Matsuda

The estimation of multiple parameters is a ubiquitous requirement in many quantum metrology applications. However, achieving the ultimate precision limit, i.e. the quantum Cram\'er-Rao bound, becomes challenging in these scenarios compared…

Quantum Physics · Physics 2024-11-25 Ben Wang , Kaimin Zheng , Qian Xie , Aonan Zhang , Liang Xu , Lijian Zhang

Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable…

Quantum Physics · Physics 2009-11-10 M. Hotta , M. Ozawa

The aim of this thesis is to develop a theoretical framework to study parameter estimation of quantum channels. We study the task of estimating unknown parameters encoded in a channel in the sequential setting. A sequential strategy is the…

Quantum Physics · Physics 2022-01-06 Vishal Katariya

As quantum tomography is becoming a key component of the quantum engineering toolbox, there is a need for a deeper understanding of the multitude of estimation methods available. Here we investigate and compare several such methods: maximum…

Quantum Physics · Physics 2019-05-22 Anirudh Acharya , Theodore Kypraios , Madalin Guta

Quantum state estimation is a fundamental task in quantum information theory, where one estimates real parameters continuously embedded in a family of quantum states. In the theory of quantum state estimation, the widely used Cram\'er Rao…

Quantum Physics · Physics 2025-07-23 Masahito Hayashi , Yingkai Ouyang

Integrated sensing and communication is regarded as a key enabler for next-generation wireless networks. To optimize the transmitted waveform for both sensing and communication, various performance metrics must be considered. This work…